View source for Whittaker transform

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The integral transform

$$F(x)=\int\limits_0^\infty(2xt)^{-1/4}W_{\lambda,\mu}(2xt)f(t)\,dt,$$

where $W_{\lambda,\mu}(z)$ is the Whittaker function (cf. [[Whittaker functions|Whittaker functions]]). For $\lambda=1/4$ and $\mu=\pm1/4$ the Whittaker transform goes over into the [[Laplace transform|Laplace transform]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  C.S. Meijer,   "Eine neue Erweiterung der Laplace-Transformation"  ''Proc. Koninkl. Ned. Akad. Wet.'' , '''44'''  (1941)  pp. 727–737</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. Doetsch,   "Handbuch der Laplace-Transformation" , '''III''' , Birkhäuser  (1973)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  E.T. Whittaker,   G.N. Watson,   "A course of modern analysis" , Cambridge Univ. Press  (1927)</TD></TR></table>